Question

What fraction of a given sample of a radioactive nuclide remains after four half-lives?

Answer 1

It is `1/16` of the original population.

Explanation:

At the beginning you have that the number of atoms is `N_0`.
After the first half lives you have `N_1=N_0/2` because by definition the half life is that time where half of the sample had the decay.
After the second half life you have `N_2=N_1/2=N_0/4`.
As you can see, after each lifetime you divide by two the original population, then after four times you divide four times for `2` that means that you divide by `2^4=16`.
So the final population `N_4=N_0/16`.